Keywords: non-linear dynamics, masonry building, seismic vulnerability, macro-models, push-over analysis, existing buildings.

The problem of the evaluation of the seismic resistance of a civil engineering structure represents a subject of high practical value but at the same time of very difficult resolution. The social and political interest on this problem, which has been underestimated for decades, has recently grown as a consequence of repetitive dramatic building failures associated to even modest earthquake events. In Italy this dramatic events have led to a total revision of the seismic codes and to a new classification of the seismic zones. Such an upgrade, which is obviously valuable, at the same time introduces new and complex problems which are relevant to structural engineering practice. In fact, in order to estimate the seismic vulnerability of an existing building and to establish if a structure requires a seismic upgrade, a structural engineer (that generally is not a researcher) requires adequate tools and sufficient knowledge. At present, structural engineers usually do not possess this knowledge. This is problematic with regard to all civil engineering structures, and with particular reference to buildings, is mainly concerned with concrete and masonry structures. For this reason, in the recent years, many authors developed simplified methodologies that should be able to simulate the non-linear seismic behaviour of masonry buildings and to provide results sufficiently accurate for engineering practice purposes. These methodologies are based on the use of simplified models [1,2,3,4] which are able to describe the behaviour of a masonry portion and for the assembly of a masonry structure; some of these methodologies are based on the use of equivalent frame models [5,6].

The aim of the present work is to define a new advanced computational tool for the simulation of the non-linear seismic behaviour of masonry buildings which is also applicable in the current engineering practice. To this purpose, starting from the simplified models available in the literature and from the experience gained with respect to the modelling of reinforced concrete walls [7], a discrete model of a portion of masonry wall has been introduced. This equivalent model, macro-element, is able to simulate the nonlinear behaviour of an entire masonry wall and of a whole building as an assemblage of several walls. The computational cost is strongly reduced when compared to a traditional finite element model. It is apparent that the effectiveness of such a macro-modelling is strongly dependent on a suitable definition of the mechanical parameters of the simplified model so that the equivalence between the continuum and the discrete models is enforced.

Since the macro-element has been designed to simulate the nonlinear mechanical behaviour of a portion of wall, a single macro-element can represent a whole masonry pier; nevertheless, the model of the masonry pier could be also realised by a mesh of macro-elements. The effectiveness of the proposed modelling has been evaluated by means of incremental static analyses carried out on masonry panels and walls which have been the object of theoretical and experimental research in the past.

1

F. Braga, D. Liberatore, "A finite element for the analysis of the response of masonry buildings", Proc. 5th North American Masonry Conference, 201-212, Urbana, 1990.

2

F. Braga, D. Liberatore, G. Spera, "A computer program for the seismic analysis of complex masonry duildings", in G.N. Pande, J. Middleton, B.Kralj (eds.), Proc. Computer Methods in Structural Masonry, 4, 309-316, Florence, 3-5 September 1997, London, E&FN spons., 1997.

3

A. Brencich and S. Lagomarsino, "A macroelement dynamic model for masonry shear walls". Proc. of the Fourth Int. Symposium on Computer Methods in Structural Masonry (STRUMAS), Firenze, 1997.

4

P. D'Asdia, A. Viskovic, "Un modello di calcolo della resistenza ultima delle pareti in muratura", Atti 6^o convegno nazionale ANIDIS, Perugia, 13-15 Ottobre 1993 (in Italian).

5

G. Magenes and G.M. Calvi, "Prospettive per la calibrazione di metodi semplificati per l'analisi sismica di pareti murarie", Convegno nazionale "La meccanica delle murature tra teoria e progetto", Messina, 18-20 Settembre, 1996 (in Italian).

6

G. Magenes, D. Bolognini, C. Braggio (eds), "Metodi semplificati per l'analisi sismica non lineare di edifici in muratura", CNR-Gruppo Nazionale per la Difesa dai Terremoti, Roma, 2000, 99 pages (in Italian)

7

I. Caliò, M. Marletta, "Seismic Performance of a Reinforced Concrete building not designed to withstand Earthquake Loading", Chapter 16 in Seismic Prevention of Damage for Mediterranean Cities A Case History: The city Catania (Italy), editor M. Maugeri, WIT press, Southampton (UK), in press (2004).

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